Bounds for Minkowski billiard trajectories in convex bodies
S Artstein-Avidan, Y Ostrover - … Mathematics Research Notices, 2014 - ieeexplore.ieee.org
In this paper, we use the Ekeland–Hofer–Zehnder symplectic capacity to provide several
bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth …
bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth …
When symplectic topology meets Banach space geometry
Y Ostrover - arXiv preprint arXiv:1404.6954, 2014 - arxiv.org
arXiv:1404.6954v1 [math.SG] 28 Apr 2014 Page 1 arXiv:1404.6954v1 [math.SG] 28 Apr 2014
When Symplectic Topology Meets Banach Space Geometry Yaron Ostrover Abstract. In this …
When Symplectic Topology Meets Banach Space Geometry Yaron Ostrover Abstract. In this …
Symplectic embeddings and the Lagrangian bidisk
VGB Ramos - 2017 - projecteuclid.org
In this article we obtain sharp obstructions to the symplectic embedding of the Lagrangian
bidisk into four-dimensional balls, ellipsoids, and symplectic polydisks. We prove, in fact, that …
bidisk into four-dimensional balls, ellipsoids, and symplectic polydisks. We prove, in fact, that …
On the Hofer–Zehnder Capacity of Twisted Tangent Bundles
J Bimmermann - 2023 - archiv.ub.uni-heidelberg.de
In this thesis, we deal with the Hofer--Zehnder capacity of disc subbundles of twisted tangent
bundles. While in the literature for most cases only the finiteness of this capacity is shown …
bundles. While in the literature for most cases only the finiteness of this capacity is shown …
Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces
J Bimmermann, L Maier - arXiv preprint arXiv:2403.06761, 2024 - arxiv.org
We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens spaces with
respect to the round metric. Interestingly we find that the Hofer-Zehnder capacity does not …
respect to the round metric. Interestingly we find that the Hofer-Zehnder capacity does not …
Periodic bounce orbits in magnetic billiard systems
AM Vocke - 2021 - archiv.ub.uni-heidelberg.de
This is an invitation to play magnetic billiards. We consider a billiard table that is an n-
dimensional compact Riemannian manifold with smooth boundary. This is a generalization …
dimensional compact Riemannian manifold with smooth boundary. This is a generalization …
Symplectic homology of disc cotangent bundles of domains in Euclidean space
K Irie - 2014 - projecteuclid.org
Let V be a bounded domain with smooth boundary in R^n, and D^*V denote its disc
cotangent bundle. We compute symplectic homology of D^*V, in terms of relative homology …
cotangent bundle. We compute symplectic homology of D^*V, in terms of relative homology …
Symplectic capacity and short periodic billiard trajectory
K Irie - Mathematische Zeitschrift, 2012 - Springer
We prove that a bounded domain Ω in\mathbb R^ n with smooth boundary has a periodic
billiard trajectory with at most n+ 1 bounce times and of length less than C nr (Ω), where C n …
billiard trajectory with at most n+ 1 bounce times and of length less than C nr (Ω), where C n …
Existence of periodic solutions in the systems of the billiard type
X Zhang, Z Cao, D Li, J Xie - Qualitative Theory of Dynamical Systems, 2021 - Springer
In this paper, a billiard type of system is studied. The system describes the motion of a
particle in a bounded domain under dissipation and periodic potential. The collisions …
particle in a bounded domain under dissipation and periodic potential. The collisions …
A Brunn–Minkowski type inequality for extended symplectic capacities of convex domains and length estimate for a class of billiard trajectories
R Jin, G Lu - Abhandlungen aus dem Mathematischen Seminar der …, 2023 - Springer
In this paper, we firstly generalize the Brunn–Minkowski type inequality for Ekeland–Hofer–
Zehnder symplectic capacity of bounded convex domains established by Artstein-Avidan …
Zehnder symplectic capacity of bounded convex domains established by Artstein-Avidan …